Properties

Label 547.2.o
Level 547
Weight 2
Character orbit o
Rep. character \(\chi_{547}(4,\cdot)\)
Character field \(\Q(\zeta_{273})\)
Dimension 6480
Newform subspaces 1
Sturm bound 91
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 547.o (of order \(273\) and degree \(144\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 547 \)
Character field: \(\Q(\zeta_{273})\)
Newform subspaces: \( 1 \)
Sturm bound: \(91\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(547, [\chi])\).

Total New Old
Modular forms 6768 6768 0
Cusp forms 6480 6480 0
Eisenstein series 288 288 0

Trace form

\( 6480q - 143q^{2} - 94q^{3} - 189q^{4} - 141q^{5} - 114q^{6} - 154q^{7} - 130q^{8} - 1178q^{9} + O(q^{10}) \) \( 6480q - 143q^{2} - 94q^{3} - 189q^{4} - 141q^{5} - 114q^{6} - 154q^{7} - 130q^{8} - 1178q^{9} - 152q^{10} - 161q^{11} - 99q^{12} - 158q^{13} - 174q^{14} - 71q^{15} - 235q^{16} - 146q^{17} + 33q^{18} - 144q^{19} - 138q^{20} - 98q^{21} - 226q^{22} - 115q^{23} - 123q^{24} - 208q^{25} - 65q^{26} + 131q^{27} - 48q^{28} - 207q^{29} - 56q^{30} - 215q^{31} - 151q^{32} - 63q^{33} - 70q^{34} - 192q^{35} - 17q^{36} - 124q^{37} - 61q^{38} - 268q^{39} - 51q^{40} + 533q^{41} + 292q^{42} - 166q^{43} - 20q^{44} + 51q^{45} - 233q^{46} - 96q^{47} - 211q^{48} - 213q^{49} + 12q^{50} - 213q^{51} - 279q^{52} - 178q^{53} + 173q^{54} - 233q^{55} + 170q^{56} - 22q^{57} + 36q^{58} - 133q^{59} + 225q^{60} - 117q^{61} - 176q^{62} + 202q^{63} + 154q^{64} - 320q^{65} - 124q^{66} - 78q^{67} + 441q^{68} + 203q^{69} - 522q^{70} - 195q^{71} + 564q^{72} - 254q^{73} + 22q^{74} - 326q^{75} - 186q^{76} - 182q^{77} - 100q^{78} - 268q^{79} - 299q^{80} - 776q^{81} - 242q^{82} + 78q^{83} + 162q^{84} - 144q^{85} - 132q^{86} - 84q^{87} + 333q^{88} - 167q^{89} - 134q^{90} - 268q^{91} - 261q^{92} - 21q^{93} + 297q^{94} - 65q^{95} - 567q^{96} + 427q^{97} - 237q^{98} + 237q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(547, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
547.2.o.a \(6480\) \(4.368\) None \(-143\) \(-94\) \(-141\) \(-154\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database